CBA arranges financing for Super Duper Pty Ltd with a 90 day bank bill with a Face Value of $500,000.   City Investments buy the bill when it is first issued at a yield of 3.25% pa and sell it 30 days later to Prudential Investments at a yield of 3.65% pa.   What price does Prudential Investments buy the bill for?

To solve this problem, we need to determine the price Prudential Investments paid for the bank bill after 30 days. Here’s a step-by-step breakdown:

### Step 1: Identify the relevant information

- **Face Value (FV)**: $500,000
- **Initial yield (City Investments)**: 3.25% per annum (pa)
- **Prudential Investments’ yield**: 3.65% per annum (pa)
- **Term of the bill**: 90 days
- **Days held by City Investments**: 30 days
- **Remaining term for Prudential Investments**: 90 days - 30 days = 60 days

### Step 2: Calculate the **Price Prudential Investments Pays**

We will use the following formula to calculate the price paid by Prudential Investments:

\[
P = \frac{FV}{1 + \left( \frac{Y \times t}{365} \right)}
\]

Where:
- $ P $ = Price paid by Prudential Investments
- $ FV $ = Face value of the bill = $500,000
- $ Y $ = Yield per annum = 3.65% or 0.0365
- $ t $ = Time remaining to maturity = 60 days
- 365 = Days in a year (assuming a standard year for these calculations)

Now, substituting the values:

\[
P = \frac{500,000}{1 + \left( \frac{0.0365 \times 60}{365} \right)}
\]

Let me calculate that.The price Prudential Investments pays for the bill is approximately **$497,017.89**.

Would you like a more detailed explanation of how the price was derived or clarification on any part of the solution? Here are 5 related questions to expand your understanding:

1. How does the change in yield affect the price of a bank bill?
2. What would happen if Prudential Investments held the bill until maturity?
3. How do you calculate the yield of a bank bill at a future date?
4. How does the time remaining to maturity impact the price of a bill?
5. What are the risks associated with investing in bank bills?

**Tip:** A higher yield typically results in a lower price, as investors are compensated through a discount to face value.

CBA arranges financing for Super Duper Pty Ltd with a 90 day bank bill with a Face Value of $500,000. City Investments buy the bill when it is first issued at a yield of 3.25% pa and sell it 30 days later to Prudential Investments at a yield of 3.65% pa. What price does Prudential Investments buy the bill for?

Learn how to calculate the price Prudential Investments pays for a $500,000 90-day bank bill at a 3.65% yield after City Investments holds it for 30 days. This finance problem explores key concepts such as discounting, interest rate calculations, and the time value of money. Suitable for undergraduate finance students or advanced high school learners.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation